Related rates: How fast is a runner going to 1st base, as seen from 2nd base?

  • #1
karush
Gold Member
MHB
3,269
5
TL;DR Summary: find how fast the distance is changing from 3rd base to a runer going to first base

Mentor note: Thread has been moved from a technical math section, so is missing the homework template.
A baseball diamond is a square with side 90 feet. A batter hits the ball and runs
toward first base with a speed of 28 feet per second.

\item [a] At what rate is his distance from second base decreasing when he is halfway to first base?

Draw a picture of the baseball diamond. The baseball player hits from home base and runs counterclockwise
towards first base. Then the player can continue counterclockwise to reach second
base, followed by third base.

so s^2=90^2+x^2

picture of field
 
Last edited by a moderator:
Physics news on Phys.org
  • #2
Look, I don't want to give you another infraction for no effort shown on your schoolwork. Your link generates an error.

Please type your work into the forum, and use the "Attach files" link to upload the diagram of the question. Thank you.
 
  • #3
berkeman said:
Look, I don't want to give you another infraction for no effort shown on your schoolwork. Your link generates an error.

Please type your work into the forum, and use the "Attach files" link to upload the diagram of the question. Thank you.
infraction????
ws07.10.png
 
Last edited by a moderator:
  • Like
Likes berkeman
  • #4
berkeman said:
Look, I don't want to give you another infraction for no effort shown on your schoolwork. Your link generates an error.

Please type your work into the forum, and use the "Attach files" link to upload the diagram of the question. Thank you.
I t tried to post a drawing but it never went thru thats parts of hw
 
  • #5
Use the "Attach files" link below the Edit window to upload a PDF or JPEG image. Please do it in a new reply. Thanks.
 
  • #6
karush said:
infraction????
Three strikes and your out!
 
  • Haha
Likes erobz and topsquark
  • #7

1. How do you set up the related rates problem for this scenario?

To set up the related rates problem, you would need to consider the distances between the bases, the speed of the runner, and the angles involved. You can use trigonometry to relate the distances and the rates of change to find the speed of the runner going to 1st base.

2. What information do you need to solve this related rates problem?

You would need the distance between 1st and 2nd base, the distance between 2nd base and the runner, the angle at which the runner is moving towards 1st base, and the speed of the runner. With this information, you can set up the necessary equations to find the speed of the runner.

3. How do you differentiate the distances and rates of change in this problem?

You would differentiate the distances with respect to time to find the rates of change. For example, if the distance between 1st and 2nd base is changing over time, you would differentiate that distance with respect to time to find the rate at which it is changing. This process allows you to relate the rates of change to find the speed of the runner.

4. Can you use similar triangles to solve this related rates problem?

Yes, you can use similar triangles to solve this related rates problem. By setting up a triangle with the bases and the runner as sides, you can use the properties of similar triangles to relate the distances and the rates of change. This approach can simplify the problem and make it easier to find the speed of the runner.

5. What are some common mistakes to avoid when solving related rates problems like this one?

Some common mistakes to avoid include not properly setting up the equations, not correctly differentiating the distances with respect to time, and not considering all the relevant information. It's important to carefully analyze the problem, identify all the variables involved, and set up the equations correctly to find the desired rate of change.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
10K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
1
Views
13K
  • Calculus and Beyond Homework Help
Replies
2
Views
6K
  • Calculus and Beyond Homework Help
Replies
16
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
2
Views
5K
  • Calculus and Beyond Homework Help
Replies
3
Views
2K
  • Calculus and Beyond Homework Help
Replies
8
Views
2K
  • Calculus and Beyond Homework Help
Replies
2
Views
6K
Back
Top